Theorem mulcomi 8185

Description: Commutative law for multiplication. (Contributed by NM, 23-Nov-1994.)

Hypotheses

Ref	Expression
axi.1	|- A e. CC
axi.2	|- B e. CC

Assertion

Ref	Expression
mulcomi	|- ( A x. B ) = ( B x. A )

Proof of Theorem mulcomi

Step	Hyp	Ref	Expression
1		axi.1	. 2 |- A e. CC
2		axi.2	. 2 |- B e. CC
3		mulcom 8161	. 2 |- ( ( A e. CC /\ B e. CC ) -> ( A x. B ) = ( B x. A ) )
4	1, 2, 3	mp2an 426	1 |- ( A x. B ) = ( B x. A )

Syntax hints:   = wceq 1397   e. wcel 2202  (class class class)co 6018   CCcc 8030   x. cmul 8037

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia3 108  ax-mulcom 8133

This theorem is referenced by:  mulcomli  8186  8th4div3  9363  numma2c  9656  nummul2c  9660  9t11e99  9740  binom2i  10911  fac3  10995  tanval2ap  12292  pockthi  12949  decsplit1  13019  decsplit  13020  sincosq4sgn  15572  2logb9irrALT  15717  2lgsoddprmlem2  15854  2lgsoddprmlem3d  15858